Algebra: Solving for X (Data Sufficiency)

Hi All,

Quick one on approach...

Question: What is a value of x?

(1) x^2 - 6 = -x

(2) x^2 = 4

This is how I tackled it...

(1) x^2 -x = 6

x = 6

(2) x^2 = 4

x = 6

So my answer would be that both (1) and (2) are sufficient to answer this question.

But no, the answer is.......

(1) x^2 - x - 6 = 0

x - 6 = 0

(x + 3)(x - 2) so x could be 3 or -2

(2) x^2 = 4

x^2 + 4 = 0

(x + 2)(x - 2)

Common across both is -2 so the answer would be a combination of 1 and 2.

My question is how does one know that they should set the equations equal to 0. Is it because the term 'solve' is used instead of.. 'What is x?'

Also I would assume that if either of the above solved to a perfect square that would be the answer?

Thanks in Advance,